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Baryogenesis by B - L g eneration due to superheavy particle decay

Baryogenesis by B - L g eneration due to superheavy particle decay. Seishi Enomoto ( Nagoya Univ , Japan ) Based on : Phys. Rev. D 84 , 096007 (2011), S. E. and Nobuhiro Maekawa (Nagoya Univ., KMI Inst.). The IOPAS HEP Theory Journal Club ＠ Academia Sinica. Introduction

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Baryogenesis by B - L g eneration due to superheavy particle decay

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  1. Baryogenesis by B - Lgenerationdue to superheavy particle decay Seishi Enomoto ( Nagoya Univ, Japan ) Based on : Phys. Rev. D 84, 096007 (2011), S. E. and NobuhiroMaekawa (Nagoya Univ., KMI Inst.) The IOPAS HEP Theory Journal Club＠ Academia Sinica

  2. Introduction • B – L violating particles and interactions • B – L number generation and bound of parameter • Summary Contents about our study 1. Introduction

  3. Introduction • In the present Universe • Matters>>Anti-matters • # Photons>># Baryons (matters) • The observation (WMAP) ( E. Komatsu [WMAP Collaboration] , Astrophys. J. Suppl. 192, 18 (2011) ) • In the Early Universe : High temperature • (the thermal fluctuation) • There exists very small asymmetry between baryons and anti-baryons. Baryons Anti- baryons Photons Not initial condition But dynamical generation Baryogenesis 1. Introduction

  4. b l • Sakharov’s 3 conditions • #B number violation • It is necessary by the definition. • C & CP violation • Baryon asymmetries do not evolve if there is no difference between particles and anti-particles. • Non-equilibrium condition • Baryon asymmetries do not evolve if the forward and back reaction rate is equal. Conditions to be evolved from toof the Universe. [A. D. Sakharov (1967) ] b decay b decay 1. Introduction

  5. X X b b b l • Sakharov’s 3 conditions • #B number violation • It is necessary by the definition. • C & CP violation • Baryon asymmetries do not evolve if there is no difference between particles and anti-particles. • Non-equilibrium condition • Baryon asymmetries do not evolve if the forward and back reaction rate is equal. Conditions in order to be evolved from toof the Universe. [A. D. Sakharov (1967) ] ** C, CP invariant case** 50 % 50 % 50 % Branching ratio 50 % X b b X b l 1. Introduction

  6. X X b l • Sakharov’s 3 conditions • #B number violation • It is necessary by the definition. • C & CP violation • Baryon asymmetries do not evolve if there is no difference between particles and anti-particles. • Non-equilibrium condition • Baryon asymmetries do not evolve if the forward and back reaction rate is equal. Conditions in order to be evolved from toof the Universe. [A. D. Sakharov (1967) ] ** C, CP invariant case** 0 % 50 % 50 % Branching ratio 100 % b X l b b #B is remained. X b l 1. Introduction

  7. Sakharov’s 3 conditions • #B number violation • It is necessary by the definition. • C & CP violation • Baryon asymmetries do not evolve if there is no difference between particles and anti-particles. • Non-equilibrium condition • Baryon asymmetries do not evolve if the forward and back reaction rate is equal. Conditions in order to be evolved from toof the Universe. [A. D. Sakharov (1967) ] b X b Suppression of the back reaction #B is remained. 1. Introduction

  8. Models of baryogenesis • GUT baryogenesis • Leptogenesis • Electro weak baryogenesis • Affleck Dine baryogenesis • etc... 1. Introduction

  9. Models of baryogenesis • GUT baryogenesis • The minimalSU(5) GUT baryogenesis • SM particles　＋　gauge bosons　＋　Colored Higgs 　　⇒#，#violating interactions • However, since #is conserved, it is known that the generated #is washed out by the sphaleron process induced after age. • Leptogenesis • Thermal leptogenesis • SM particles　＋　Right handed neutrinos 　⇒　#is conserved, but #, #are violated. • After that, a part of # is converted to #by the sphaleron process. ★Both models are heavy particles decay scenario, and more, just simple. ★Deciding the success is whether #is violated or not. [M. Yoshimura (1978), S. Weinberg (1979) , etc. ] Is there any possibilities to generate #B - Lwith heavy particles? [M. Fukugita, T. Yanagida(1986) ] 1. Introduction

  10. Introduction • B – L violating particles and interaction • B – L number generation and bound of parameter • Summary Contents about our study 1. Introduction 2. B – L violatingparticle & int.

  11. Decomposition of the, violating interactions • There exists , in the higher dimensional interactions. decomposition of a interaction ⇒obtationed or particles and interactions • dim. 5 : ⇒　Leptogenesis • dim. 6 : ⇒　GUT baryogenesis ★ We can obtain the scenario to generate #to decompose the violating higher dimensional interactions! 2. B – L violatingparticle & int.

  12. What does exist as the violating interactions in the SM? • dim. 5 : ⇒ Leptogenesis • dim. 6 : Nothing… • dim. 7 : ※ Using the SU(5) representation,[ , , ] differential interactions： mass of the SM particles　 ⇒　 We ignore after this. using E.O.M. 2. B – L violatingparticle & int.

  13. Decomposition of dim. 7 interactions These particles play a role to violate #!! mediated mediated a scalar boson a vector boson mediateda fermion • ★Summary of the mediated particle scalar: , , , , fermion: , , , , , vector: , , ⇒ number generation 2. B – L violatingparticle & int.

  14. Decomposition of dim. 7 interaction These particles play a role to violate # !! • etc… • etc… mediated mediated a scalar boson a vector boson mediateda fermion Focus on! • ★Summary of the mediated particle scalar: , , , , fermion: , , , , , vector: , , ⇒ number generation 2. B – L violatingparticle & int.

  15. Higher dimensional interaction mediated a scalar , (1) • Components (Charges are same to the SM fermions.) , • An example : 2. B – L violatingparticle & int.

  16. Higher dimensional interaction mediated a scalar ,(2) • An example of an example（7 dim. --> 4 dim. + 5 dim.） generated # ■dim. 4 : ■dim. 5 : ✂ violating interaction!! 2. B – L violatingparticle & int.

  17. Higher dimensional interaction mediated a scalar ,(3) • dim. 4(3point interactions) • dim. 5(4 point interactions) • #generated by the decay SM , SM SM , SM , 2. B – L violatingparticle & int.

  18. Higher dimensional interaction mediated a scalar ,(3) • dim. 4(3point interactions) • dim. 5(4 point interactions) • #generated by the decay • Sakharov’s 3 conditions • #B number violation • It is necessary by definition. • C & CP violation • Baryon asymmetries do not evolve if there is no difference between particles and anti-particles. • Non-equilibrium condition • Baryon asymmetries do not evolve if the forward and back reaction rate is equal. [A. D. Sakharov (1967) ] #B – L violating interactions (4 dim. & 5 dim. Int. with ) + The sphaleron process SM , SM SM , SM , 2. B – L violatingparticle & int.

  19. Higher dimensional interaction mediated a scalar ,(3) • dim. 4(3point interactions) • dim. 5(4 point interactions) • #generated by the decay • Sakharov’s 3 conditions • #B number violation • It is necessary by definition. • C & CP violation • Baryon asymmetries do not evolve if there is no difference between particles and anti-particles. • Non-equilibrium condition • Baryon asymmetries do not evolve if the forward and back reaction rate is equal. [A. D. Sakharov (1967) ] #B – L violating interactions (4 dim. & 5 dim. Int. with ) + The sphaleron process SM , SM SM , SM , 2. B – L violatingparticle & int.

  20. Introduction • B – L violating particles and interactions • B – L number generation and bound of parameter • Summary Contents about our study 2. B – L violatingparticle & int. 3. #B – L generation & bound

  21. Characteristic quantity for the generated # • the mean netnumber This parameter means how many # is generated by a pair of & . , , , , , : decay mode of , : branching ratio, : #in the final state • #generated by the particle (in case that all particles decay) # ： 3. #B – L generation & bound

  22. Evaluation of the mean net #(1) ( , : dimensionless coupling constant, : cut-off scale ) , , , , (SM) (SM) (SM) (SM) or Trace : Taken about the SM fermion labels (a,b) decay width ， 2 body decay 3body decay loop function Interference term 3. #B – L generation & bound

  23. Evaluation of the mean net #(2) • Approximation (assuming) • We evaluate the trace part with only one dominant term. And we rewrite the dominant term as . • Moreover, , • O • 2 body decay3 body decay ⇒ ) ★, 3. #B – L generation & bound

  24. Evaluation of the mean net #(2) • Approximation (assuming) • Considering only dominant coupling among some , • Moreover, , • O • 2 body decay3 body decay (so that, ) ★, • Sakharov’s 3 conditions • #B number violation • It is necessary by definition. • C & CP violation • Baryon asymmetries do not evolve if there is no difference between particles and anti-particles. • Non-equilibrium condition • Baryon asymmetries do not evolve if the forward and back reaction rate is equal. [A. D. Sakharov (1967) ] #B – L violating interactions (4 dim. & 5 dim. Int. with ) + The sphaleron process , O Assumed 3. #B – L generation & bound

  25. Evaluation of the mean net #(2) • Approximation (assuming) • Considering only dominant coupling among some , • Moreover, , • O • 2 body decay3 body decay (so that, ) ★, • Sakharov’s 3 conditions • #B number violation • It is necessary by definition. • C & CP violation • Baryon asymmetries do not evolve if there is no difference between particles and anti-particles. • Non-equilibrium condition • Baryon asymmetries do not evolve if the forward and back reaction rate is equal. [A. D. Sakharov (1967) ] #B – L violating interactions (4 dim. & 5 dim. Int. with ) + The sphaleron process , O Assumed 3. #B – L generation & bound

  26. Bounds for parameters • We consider about 2 situations for the violating particle species which can generate the baryon number in the Universe. • Case A : thermal produced • The particle species which can generate the #is produced thermally, and after that, it is freezed-out from the thermal bath, and then decay. • Case B : non-thermal produced + energy dominant • There exists many number of the particle species which dominates the energy in the Universe, and after that, It decays. , , , , Universe Others Others Others decay (thermally) (decoupled) , , Universe ? Others Others , decay (non-thermally produced ) (Many entropies are produced.) 3. #B – L generation & bound

  27. Bounds for parameters • Case A : is generated thermally • A limit to 3 point coupling constant • Using the observational value : ↓ Others Others Others , , : entropy density • ※ Generically, the relic abundance • is reduced fromthe thermal relic. d.o.f. of The transition rate from # to #by the sphaleron process [ J. A. Harvey and M. S. Turner (1990) ] d.o.f. of rela. particles • ：the reduced ratio of • fromthe thermal relic • abundance SM , SM 3. #B – L generation & bound

  28. Bounds for parameters • Case A : is generated thermally • A bound for the mass • NOTE : is applicable if , pair annihilation does not happen. → 　＠ the decay temperature of : • Other parameters • In case , Others Others Others , , • : the thermal averaged cross section (times the velocity) • : the Plank mass（） ( ※ Corresponding to ) ( : , : ) What’s the value or the bound of ? • ・↓ ⇒ ↑ ⇒ ’s lifetime becomes shorter. • ・ The bound exists at which the lifetime becomes shorter than the freeze-out time scale. 3. #B – L generation & bound

  29. Bounds for parameters • Case A : is generated thermally • freeze-out taking into account only the scattering due to the gauge interaction (without the decay) • Boltzmann equation • Values of &when Others Others Others , , • ・ • ・ : -th modified Bessel func. 3. #B – L generation & bound

  30. Bounds for parameters • Case A : is generated thermally • ■Boltzmann eq. with the decay ★ a lower boud exists Others Others Others , , (a) (b) (c) • ・ 3. #B – L generation & bound

  31. Others Others , • Bounds for parameters • Case B : ’senergy dominates in the Universe • A lot of entropies are generated by ’s decay. • We impose the additional condition ＠ as in case A ⇒　 • ①& ② lead to a lower mass bound : : reheating temperature by , decay • , Observational value : ・・・① ・・・② 3. #B – L generation & bound

  32. Others Others , • Bounds for parameters • Case B : ’senergy dominates in the Universe • Other parameters in case • These results are not so different compared with Case A. 3. #B – L generation & bound

  33. Others Others , • Bound for parameters • Case B : ’senergy dominates in the Universe • Other parameters in case • These results are not so different compared with Case A. • Sakharov’s 3 conditions • #B number violation • It is necessary by definition. • C & CP violation • Baryon asymmetries do not evolve if there is no difference between particles and anti-particles. • Non-equilibrium condition • Baryon asymmetries do not evolve if the forward and back reaction rate is equal. [A. D. Sakharov (1967) ] #B – L violating interactions (4 dim. & 5 dim. Int. with ) + The sphaleron process , O Assumed Decay in out-of-equilibrium * Case A : decay after freeze-out * Case B : non-thermal state Imposing 3. #B – L generation & bound

  34. Others Others , • Bound for parameters • Case B : ’senergy dominates in the Universe • Other parameters in case • These results are not so different compared with Case A. • Sakharov’s 3 conditions • #B number violation • It is necessary by definition. • C & CP violation • Baryon asymmetries do not evolve if there is no difference between particles and anti-particles. • Non-equilibrium condition • Baryon asymmetries do not evolve if the forward and back reaction rate is equal. [A. D. Sakharov (1967) ] #B – L violating interactions (4 dim. & 5 dim. Int. with ) + The sphaleron process , O Assumed Decay in out-of-equilibrium * Case A : decay after freeze-out * Case B : non-thermal state Imposing 3. #B – L generation & bound

  35. B violating interaction --> proton decay • Rough estimation of the proton’s (partial) decay rate : The current bound : ※ This is because the B violating interaction comes from dim.7 operator. enough stable! Saying exactly, this interaction is not sizable for the proton decay. 3. #B – L generation & bound

  36. Introduction • B – L violating particles and interactions • B – L number generation and bound of parameter • Summary Contents about our study 3. #B – L generation & bound 4. Summary

  37. Summary • We have shown the new scenario generating which was obtained from dim. 7 interactions in SM. • The particles with the violating interactions are in the representation of , , , which are scalar bosons, , , , , which are fermions, , which are vector bosons of , • In particular, we have focused on the bosons of and (components : , , , , ), and we have shown the concrete interactions. • We have evaluated the mean net #by the decay of , , , , , and then we have limited to some parameters (yukawa couplings, masses, or so) with some approximation and the observational #. • Case A: thermal produced , , • Case B : non-thermal + energy dominant , ( ⇔) 4. Summary

  38. back up

  39. Sakharov’s 3 conditions • #B number violation • It is necessary by the definition. • C & CP violation • Baryon asymmetries do not evolve if there is no difference between particles and anti-particles. • Non-equilibrium condition • Baryon asymmetries do not evolve if the forward and back reaction rate is equal. These are needed to be evolved from toof the Universe. [A. D. Sakharov (1967) ] b X b 1. Introduction

  40. b l • Sakharov’s 3 conditions • #B number violation • It is necessary by definition. • C & CP violation • Baryon asymmetries do not evolve if there is no difference between particles and anti-particles. • Non-equilibrium condition • Baryon asymmetries do not evolve if the forward and back reaction rate is equal. Conditions to be evolved from toof the Universe. [A. D. Sakharov (1967) ] b b 1. Introduction

  41. Sakharov の 3 条件 • バリオン数の破れ • 定義から必要 • C & CP の破れ • 粒子・反粒子の反応に差がなければバリオン非対称性は発展しない • 非平衡反応 • 反応と逆反応が同じ速さで進むとバリオン非対称性は発展しない の宇宙から でない 宇宙に発展するための条件 [A. D. Sakharov (1967) ] b b 1. Introduction

  42. dim. 7 相互作用項の分解 スカラーボソン：, 　フェルミオン：, ベクトルボソン：, スカラーボソン：, , , , , 　フェルミオン：, , , , ベクトルボソン：, , , , , スカラー，ベクトル：, , , , , 　フェルミオン：, , , , , ,

  43. Decomposition of dim. 7 interaction (1) mediated a scalar boson：, , , , , , , , , , , , , , mediated a vector boson：, , , , mediateda fermion：, , ,, 2. B – L violatingparticle & int.

  44. Decomposition of dim. 7 interaction (2) scalar boson, fermion, vector boson scalar boson, vector boson fermion : , , , , ★Summary of the mediated particle These particles play a role to violate # !! ：, : , , , , , scalar, vector: , , , , , fermion: , , , , , , 2. B – L violatingparticle & int.

  45. etc… • etc… • Decomposition of dim. 7 interaction (2) scalar boson, fermion, vector boson scalar boson, vector boson fermion : , , , , ★Summary of the mediated particle These particles play a role to violate # !! ：, : , , , , , Focus on! scalar, vector: , , , , , fermion: , , , , , , ⇒ number generation 2. B – L violatingparticle & int.

  46. Decomposition of dim. 7 interaction (1) , , , , mediated a scalar boson mediated a vector boson , , , , mediateda fermion 2. B – L violatingparticle & int.

  47. Decomposition of dim. 7 interaction (1) , , , , mediated a scalar boson mediated a vector boson , , , , mediateda fermion 2. B – L violatingparticle & int.

  48. Decomposition of dim. 7 interaction (1) , , , , , , , , 2. B – L violatingparticle & int.

  49. スカラー ,を媒介する高次相互作用 • ,

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